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Graph Eigenfunctions and Quantum Unique Ergodicity

2010/06/18 by Shimon Brooks, Elon Lindenstrauss, Brooks, Shimon +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Spectral Theory in Mathematical Physics #math.DS

paper · pdf · doi:10.48550/arxiv.1006.3583

8 pages

arxiv created 2010/06/18 · openalex publication_date 2010/06/18 · arxiv updated 2010/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the techniques of our previous paper to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of ℍ×ℍ. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with prior work of the second named author, this implies Quantum Unique Ergodicity for such functions.

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